Chance is often defined as the opposite of Necessity. The English word derives from the Latin cadere - to fall, especially cadens a fall, falling.

Dictionary definitions refer to the fall of the dice, but the etymology suggests it is related to the grammatical idea of declension, which describes the falling or "leaning" away of the genitive, dative, and accusative cases from the "straight up" nominative case. The word connotes falling in the sense of decadence. Note the German for chance is Zufall.

The first thinker to suggest a physical explanation for chance in the universe was Epicurus. Epicurus was influenced strongly by Aristotle, who regarded chance as a fifth cause. He said there must be cases in which the normally straight paths of atoms in the universe occasionally bend a little and the atoms "swerve" to prevent the universe and ourselves from being completely determined by the mechanical laws of Democritus.

Despite abundant evidence, many philosophers deny that real chance exists. If a single event is determined by chance, then indeterminism would be true, they say, and undermine the very possibility of certain knowledge. Some go to the extreme of saying that chance makes the state of the world totally independent of any earlier states, which is nonsense, but it shows how anxious they are about chance.

The Stoic Chrysippus (200 B.C.E.) said that a single uncaused cause could destroy the universe (cosmos), a concern shared by some modern philosophers, for whom reason itself would fail.

Everything that happens is followed by something else which depends on it by causal necessity. Likewise, everything that happens is preceded by something with which it is causally connected. For nothing exists or has come into being in the cosmos without a cause. The universe will be disrupted and disintegrate into pieces and cease to be a unity functioning as a single system, if any uncaused movement is introduced into it.

The core idea of chance and indeterminism is closely related to the idea of causality. Indeterminism for some is simply an event without a cause, an uncaused cause or causa sui that starts a new causal chain. If we admit some uncaused causes, we can have an adequate causality without the physical necessity of strict determinism - which implies complete predictability of events and only one possible future.

An example of an event that is not strictly caused is one that depends on chance, like the flip of a coin. If the outcome is only probable, not certain, then the event can be said to have been caused by the coin flip, but the head or tails result itself was not predictable. So this "soft" causality, which recognizes prior uncaused events as causes, is undetermined and the result of chance alone.

Even mathematical theorists of games of chance found ways to argue that the chance they described was somehow necessary and chance outcomes were actually determined. The greatest of these, Pierre-Simon Laplace, preferred to call his theory the "calculus of probabilities." With its connotation of approbation, probability was a more respectable term than chance, with its associations of gambling and lawlessness. For Laplace, the random outcomes were not predictable only because we lack the detailed information to predict. As did the ancient Stoics, Laplace explained the appearance of chance as the result of human ignorance. He said,

"The word 'chance,' then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order."

Decades before Laplace, Abraham de Moivre had discovered the normal distribution (the bell curve) of outcomes for ideal random processes, like the throw of dice. Perfectly random processes produce a regular distribution pattern for many trials (the law of large numbers). Inexplicably, the discovery of these regularities in various social phenomena led Laplace and others to conclude that the phenomena were determined, not random. They simply denied chance in the world.

Chance is closely related to the ideas of uncertainty and indeterminacy. Uncertainty today is best known from Werner Heisenberg's principle in quantum mechanics. It states that the exact position and momentum of an atomic particle can only be known within certain (sic) limits. The product of the position error and the momentum error is equal to a multiple of Planck's constant of action. This irreducible randomness in physical processes established the existence of chance and indeterminism in the world.

But real chance and uncertainty had already entered physics fifty years earlier than Heisenberg, when Ludwig Boltzmann showed in 1877 that random collisions between atomic particles in a gas could explain the increase in entropy that is the Second Law of Thermodynamics.

In 1866, when Boltzmann first derived Maxwell's velocity distribution of gas particles, he did it assuming that the physical motion of each particle (or atom) was determined exactly by Newton's laws. In 1872, when he showed how his kinetic theory of gases could explain the increase in entropy, he again used strictly deterministic physics. But Boltzmann's former teacher Josef Loschmidt objected to his derivation of the second law. Loschmidt said that if time was reversed, the deterministic laws of classical mechanics require that the entropy would go down, not up.

So in 1877 Boltzmann reformulated his derivation, assuming that each collision of gas particles was not determined, but random. He assumed that the directions and velocities of particles after a collision depended on chance, as long as energy and momentum were conserved. He could then argue that the particles would be located randomly in "phase space" based on the statistical assumption that individual cells of phase space were equally probable. His H-Theorem produced a quantity which would go only up, independent of the time direction. Laws of nature became statistical. Max Born put statistical mechanics on a firm quantum mechanical basis in 1926, when he showed that Schrödinger's deterministic equation for the wave function predicts only probabilities for directions after an electron collision.

Boltzmann's student Franz S. Exner defended the idea of absolute chance and indeterminism as a hypothesis that could not be ruled out on the basis of observational evidence. Exner did this in his 1908 inaugural lecture at Vienna University as rector (two years after Boltzmann's death), and ten years later in a book written during World War I. But Exner's view was not the standard view. Ever since the eighteenth-century development of the calculus of probabilities, scientists and philosophers assumed that probabilities and statistical phenomena, including social statistics, were completely determined. They thought that our inability to predict individual events was due simply to our ignorance of the details.

In his 1922 inaugural address at the University of Zurich, What Is a Law of Nature?, Erwin Schrödinger said about his teacher,

"It was the experimental physicist, Franz Exner, who for the first time, in 1919, launched a very acute philosophical criticism against the taken-for-granted manner in which the absolute determinism of molecular processes was accepted by everybody. He came to the conclusion that the assertion of determinism was certainly possible, yet by no means necessary, and when more closely examined not at all very probable.

"Exner's assertion amounts to this: It is quite possible that Nature's laws are of thoroughly statistical character. The demand for an absolute law in the background of the statistical law — a demand which at the present day almost everybody considers imperative — goes beyond the reach of experience."

[Ironically, just four years later, after developing his continuous and deterministic wave theory of quantum mechanics, Schrödinger would himself "go beyond the reach of experience" searching for deterministic laws underlying the discontinuous, discrete, statistical and probabilistic indeterminism of the Bohr-Heisenberg school, to avoid the implications of absolute chance in quantum mechanics. Planck and Einstein too were repulsed by randomness and chance. "God does not play dice," was Einstein's famous remark.]

A major achievement of the Ages of Reason and Enlightenment was to banish absolute chance as unintelligible and atheistic. Newton's Laws provided a powerful example of deterministic laws governing the motions of everything. Surely Leucippus' and Democritus' original insights had been confirmed.

In 1718 Abraham De Moivre wrote a book called The Doctrine of Chances. It was very popular among gamblers. In the second edition (1738) he derived the mathematical form of the normal distribution of probabilities, but he denied the reality of chance. Because it implied events that God could not know, he labeled it atheistic.

Chance, in atheistical writings or discourse, is a sound utterly insignificant: It imports no determination to any mode of existence; nor indeed to existence itself, more than to non existence; it can neither be defined nor understood.

As early as 1784, Immanuel Kant had argued that the regularities in social events from year to year showed that they must be determined.

"Thus marriages, the consequent births and the deaths, since the free will seems to have such a great influence on them, do not seem to be subject to any law according to which one could calculate their number beforehand. Yet the annual (statistical) tables about them in the major countries show that they occur according to stable natural laws."

In the early 1800's Adolphe Quetelet and Henry Thomas Buckle argued that these regularities in social physics proved that individual acts like marriage and suicide were determined by natural law.

Franz Exner was not alone in defending chance before quantum uncertainty. In the nineteenth century in America, Charles Sanders Peirce coined the term "tychism" for his idea that absolute chance was the first step in three steps to "synechism" or continuity.

Quetelet and Buckle thought they had established an absolute deterministic law behind all statistical laws. Buckle went so far as to claim it established the lack of free will.

Renouvier and Fouillee introduced chance or indeterminism simply to contrast it with determinism, and to discover some way, usually a dialectical argument like that of Hegel, to reconcile the opposites. Renouvier argues for human freedom, but nowhere explains exactly how chance might contribute to that freedom, other than negating determinism.

Maxwell may have used the normal distribution of Quetelet and Buckle's social physics as his model for the distribution of molecular velocities in a gas. Boltzmann also was impressed with the distribution of social statistics, and was initially convinced that individual particles obeyed strict and deterministic Newtonian laws of motion.

Peirce does not explain much with his Tychism, and with his view that continuity and evolutionary love is supreme, may have had doubts about the importance of chance. Peirce did not propose chance as directly or indirectly providing free will. He never mentions the ancient criticisms that we cannot accept responsibility for chance decisions. He does not really care for chance as the origin of species, preferring a more deterministic and continuous lawful development, under the guidance of evolutionary love. But Peirce does say clearly, well before Exner, that the observational evidence simply does not establish determinism.

It remained for William James, Peirce's close friend, to assert that chance can provide random unpredictable alternatives from which the will can choose or determine one alternative. James was the first thinker to enunciate clearly a two-stage decision process, with chance in a present time of random alternatives, leading to a choice which selects one alternative and transforms an equivocal ambiguous future into an unalterable determined past. There are undetermined alternatives followed by adequately determined choices.

"The stronghold of the determinist argument is the antipathy to the idea of chance...This notion of alternative possibility, this admission that any one of several things may come to pass is, after all, only a roundabout name for chance...

What is meant by saying that my choice of which way to walk home after the lecture is ambiguous and matter of chance?...It means that both Divinity Avenue and Oxford Street are called but only one, and that one either one, shall be chosen." (James, The Dilemma of Determinism, in The Will to Believe, 1897, p.155)

Chance is critically important for the question of free will because strict necessity implies just one possible future. Absolute chance means that the future is fundamentally unpredictable at the levels where chance is dominant. Chance allows alternative futures and the question becomes how the one actual present is realized from these potential alternative futures.

The amount of chance and the departure from strict causality required for free will is very slight compared to the miraculous ideas often associated with the "causa sui" (self-caused cause) of the ancients. For medieval philosophers, only God could produce a causa sui, a miracle. Modern quantal randomness, unless amplified to the macroscopic world, is often insignificant, not a miracle at all.

Despite David Hume's critical attack on causality, many philosophers embrace causality strongly, including Hume himself in his other writings, where he dogmatically asserts "'tis impossible to admit of any medium betwixt chance and an absolute necessity." Since Chrysippus twenty-two centuries ago, philosophers still connect causality to the very possibility of logic and reason.

Bertrand Russell said "The law of causation, according to which later events can theoretically be predicted by means of earlier events, has often been held to be a priori, a necessity of thought, a category without which science would not be possible." (Russell, External World p.179) Although he felt some claims for causality might be excessive, Russell was unwilling to give up strict determinism, saying "Where determinism fails, science fails."(Determinism and Physics, p.18)

Henri Poincaré said "Every phenomenon, however trifling it be,
has a cause, and a mind infinitely powerful and
infinitely well-informed concerning the laws of nature
could have foreseen it from the beginning of the ages.
If a being with such a mind existed, we could play
no game of chance with him ; we should always lose.
For him, in fact, the word chance would have no
meaning, or rather there would be no such thing as
chance."

We know that even in a world with microscopic chance, macroscopic objects are determined to an extraordinary degree. Newton's laws of motion are deterministic enough to send men to the moon and back. In our Cogito model, the Macro Mind is macroscopic enough to ignore quantum uncertainty for the purpose of the reasoning will. The neural system is robust enough to insure that mental decisions are reliably transmitted to our limbs.

We call this kind of determinism "adequate determinism." Despite quantum uncertainty, the world is adequately determined to send men to the moon. Quantum uncertainty leads some philosophers to fear an undetermined world of chance, one where Chrysippus' imagined collapse into chaos would occur and reason itself would fail us. But the modest indeterminism required for free will is no chaotic irrational threat, since most physical and mental events are overwhelmingly "adequately determined."

There is no problem imagining that the three traditional mental faculties of reason - perception, conception, and comprehension - are all carried on with "adequate determinism" in a physical brain where quantum events and thermal noise do not interfere with normal operations.

There is also no problem imagining a role for chance in the brain in the form of quantum level noise (as well as pre-quantal thermal noise). Noise can introduce random errors into stored memories. Noise could create random associations of ideas during memory recall. Many scientists have speculated that this randomness may be driven by microscopic fluctuations that are amplified to the macroscopic level. This would not happen in some specific location in the brain. It is most likely a general property of all neurons.

We distinguish seven increasingly sophisticated ideas about the role of chance and indeterminism in the question of free will. Many libertarians have accepted the first two. Determinist and compatibilist critics of free will make the third their central attack on chance, claiming that it denies moral responsibility. But very few thinkers appear to have considered all seven essential requirements for chance to contribute to libertarian free will.

Chance can only generate random (unpredictable) alternative possibilities for action or thought. The choice or selection of one action must be adequately determined, so that we can take responsibility. And once we choose, the connection between mind/brain and motor control must be adequately determined to see that "our will be done."

Chance, in the form of noise, both quantum and thermal noise, must always be present. The naive model of a single random microscopic event, amplified to affect the macroscopic brain, never made sense. Under what ad hoc circumstances, at what time, at what place in the brain, would it occur to affect a decision?

To the extent that chance is not completely suppressed by the will, the resulting choice can be considered to have an element of randomness. The agent can still take responsibility for allowing the choice to be partially or completely random, the equivalent of flipping a mental coin.

Of those thinkers who have considered most of these aspects of chance, a small fraction have also seen the obvious parallel with biological evolution and natural selection, with its microscopic quantum accidents causing variations in the gene pool and macroscopic natural selection of fit genes by their reproductive success.

Our Macro Mind needs the Micro Mind for the free action items and thoughts in an Agenda of alternative possibilities to be de-liberated by the will. Chance in the Micro Mind is the "free" in free will and the source of human creativity. The adequately determined Macro Mind is the "will" in free will that de-liberates, choosing actions for which we can be morally responsible.

The Etymology of Chance

The ancient philosophers used a small number of words to express important philosophical concepts like chance and necessity. Tracing the etymology back to proto-Indo-European produces some surprising insights into what the ancients may have been thinking.

We are not certain of the exact words used by Epicurus to describe his "swerve" of the atoms. But since the swerve is critically important in the first version of libertarian freedom, it is worth investigating the root meanings for the words Epicurus and Lucretius used.

All these words carry strong connotations of moral responsibility. More specifically, the connotations for cases (other than the nominative) are negative, of straying from the straight path, of leaning, bending, and falling. By contrast, the nominative is standing upright (ὀρθή - ortho), straight and direct (εὐθεῖα).

Now falling was the fundamental notion of the grammarians (e.g., Dionysius Thrax), when they describe all the cases as declining or falling from the nominative case. The Greek word for case is πτῶσις (to fall), the Latin casus, from cadere (to fall). The German Fall is the origin of our word fall.

In English, we inflect nouns, showing that they bend away from the nominative case. In German, Beugung, means bending in the sense of bending the law to pervert justice. We decline the nouns in Latin. As a result, the grammatical cases imply decadence. They are crooked, where the nominative is straight.

The accusative case is very interesting, because the root meaning is (toward the) cause (ad causa). The word "accuse" has all the implications of legal and moral responsibility. In Greek the αιτία are the explanatory causes responsible for an event.

Our English word for chance derives from Latin cadentia. Some take it to mean the fall of the dice in a game of chance, but it seems equally plausible that the idea of falling away from the upright direction of the nominative is also a source of the meaning.

This might explain what Epicurus means when he says an atom "swerves" on occasion. He means it departs from the upright nominative case. The Greek κλίνειν means to lean. Lucretius uses declinando and Cicero inclinando.

Let's look more critically at what Epicurus may have said, according to Lucretius and Cicero especially.

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The Rise of Statistical Thinking, 1820-1900, by Theodore Porter, (Princeton, 1986) p.219-247, tells how Charles Sanders Peirce embraces chance as "Tychism." Porter also provides a summary of the influences of Renouvier, Fouillee, and Joseph Delbouef on Peirce.

The Taming of Chance, by Ian Hacking, (Cambridge, 1990) p.11, tells how Peirce attacked the doctrine of necessity. Hacking's thesis is that there was an "erosion of determinism" in the nineteenth century culminating in Peirce.

Henri Poincare

"To begin with, what is chance? The ancients
distinguished between the phenomena which seemed
to obey harmonious laws, established once for all,
and those that they attributed to chance, which were
those that could not be predicted because they were
not subject to any law. In each domain the precise
laws did not decide everything, they only marked
the limits within which chance was allowed to move.
In this conception, the word chance had a precise,
objective meaning; what was chance for one was
also chance for the other and even for the gods.

"But this conception is not ours. We have become
complete determinists, and even those who wish to
reserve the right of human free will at least allow
determinism to reign undisputed in the inorganic
world. Every phenomenon, however trifling it be,
has a cause, and a mind infinitely powerful and
infinitely well-informed concerning the laws of nature
could have foreseen it from the beginning of the ages.
If a being with such a mind existed, we could play
no game of chance with him; we should always lose.

"For him, in fact, the word chance would have no
meaning, or rather there would be no such thing as
chance." (Science and Method, Henri Poincare, p.64)

Max Planck

"Just as no physicist will in the last resort acknowledge the play of chance in human nature, so no physiologist will admit the play of chance in the absolute sense." Max Planck, Where Is Science Going, p.147.

"the assumption of chance in inorganic nature is incompatible with the working principle of natural science." Max Planck, Where Is Science Going, p.154.